FACULTY of ARTS AND SCIENCESDEPARTMENT OF STATISTICS
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### Courses

STAT 153 Probability I (3-2) 4

Sample space, events. Basic combinatorial probability, conditional probability. Bayes’ theorem, independence, random variables, distributions, expectation.

STAT 154 Probability II (3-2) 4

Transformations of random variables, generating functions, conditional expectation. Limit theorems, central limit theorem, limiting distributions.

Prerequisite: STAT 153, MATH 119

STAT 155 Principles of Statistics (3-2) 4

Brief history of statistics. Basic definitions and types of data, descriptive statistics. Elementary probability, random variables, probability distributions and their properties.  Introduction to use of computer solving tools.

STAT 156 Statistical Methods (3-2) 4

Sampling distributions, estimation, confidence intervals, hypothesis testing, power of test, analysis of variance for one or two factor designs, linear regression, basic nonparametric procedures.  Elementary time series analysis, trends, seasonality, forecasting.

Prerequisite: STAT 155

STAT 201 Introduction to Probability and Statistics I (3-0) 3

Experiments and events. Set theory. Axioms and basic theorems of probability. Finite sample spaces and counting techniques. Independent events. Conditional probability. Random variables and distributions. Expectation, variance, covariance and correlation. Some special distributions.

STAT 202 Introduction to Probability and Statistics II (3-0) 3

Random samples. Sample mean and variance. Chebychev's inequality. Law of large numbers. Central limit theorem. Estimation. Maximum likelihood, unbiased, minimum variance unbiased, consistent and efficient estimators. Sufficiency. Confidence intervals. Hypothesis testing. Introduction to nonparametric methods. Regression and analysis of variance.

Prerequisite: STAT 201

STAT 221 Fundamentals of Statistics (3-0) 3

Introduction to probability. Finite sample spaces. Conditional probability and independence. Discrete and continuous random variables. Random sample and statistics. Statistical inference, estimation and tests of hypotheses. Simple linear regression.

Prerequisite: MATH 120

STAT 256 Numerical Methods (3-2) 4

Accuracy in numerical computations. Numerical solution of linear and nonlinear algebraic equations. Finding eigen-values and eigenvectors. Finite difference calculus. Interpolation and extrapolation. Numerical differentiation and integration. Numerical approximation methods.

Prerequisite: STAT 291 or STAT 292, MATH 260

STAT 271 Mathematical Statistics I  (3-2) 4

Common theoretical distributions. Sampling distributions.  Principles of point estimation. Techniques of estimation .Properties of point estimators. Optimality criteria in estimation. Selected topics from robust inference. Bayesian inference.

Prerequisite: STAT 154, MATH 120

STAT 272 Mathematical Statistics II  (3-2) 4

Region (interval) estimation. Hypothesis testing.  Optimality properties for hypothesis testing. Likelihood ratio tests. Sequential tests.

Prerequisite: STAT 271

STAT 291 Statistical Computing I (3-2) 4

Introduction to statistical techniques in statistical software. Managing and analyzing data using statistical database packages. Introduction to MATLAB with applications to matrix algebra.

Prerequisite: CENG 230, STAT 156.

STAT 292 Statistical Computing II (3-2) 4

Introduction to programming and computation. Introduction to computer organization and basic data structures. An advanced programming language with applications to statistical procedures.

Prerequisite: CENG 230

STAT 356 Statistical Data Analysis (3-2) 4

Types of data. Graphical and tabular represantation of data. Approaches to finding the unexpected in data. Exploratory data analysis for large and high-dimensional data. Analysis of categorical data. Elements of robust estimation. Handling missing data. Smoothing methods. Data mining.

Prerequisite: STAT 156, STAT 291

STAT 361 Computational Statistics (3-2) 4

Random number generation. Generating from other distributions. Monte Carlo methods for inferential statistics. Resampling. Data partitioning. Cross-validation. Bootstraping. Jackknifing. Tools for exploratory and graphical data analysis. Nonparametric probability density estimation.

Prerequisite: STAT 291

STAT 363 Linear Models I (3-2) 4
Simple and Multiple Linear Regression Models.  Estimation ,  interval estimation and test of hypothesis on the parameters of the models. Model Adequecy Checking. Multicollinearity. Transformation.

Prerequisite: MATH 260, STAT 156

STAT 364 Linear Models II (3-2) 4
Simple nonlinear models. Less than full rank models : One- way , Two-way ANOVA models, Split Plot Design,  Random Effect Models,  Analysis of Covariance Model. Introduction to generalized linear models.

Prerequisite: STAT 363

STAT 365 Survey Sampling Techniques (3-2) 4

Introduction to survey sampling. Probability sampling techniques. Simple random sampling. Stratified element sampling. Systematic sampling. Equal sized cluster sampling. Unequal sized cluster sampling. PPS selection techniques. Sampling errors.

Prerequisite: STAT 156 or equivalent for non-statistics majors.

STAT 366 Survey Research Methods (3-0) 3

Introduction to survey research. Survey research methods. Planning of sample surveys. Survey designs. Methods of data collection. Questionnaire design techniques. Fieldwork organization methods. Survey designs over time. Multiplicity survey designs. Establishment survey designs. Components of total survey error. Survey research project.

Prerequisite: STAT 365 or consent of department for non-statistics majors.

STAT 376 Stochastic Processes  (3-2) 4

Random walk. Markov chains, martingales. Discrete and continuous parameter Markov processes.  Branching processes. Birth and death processes. Renewal processes. Queuing processes. Applications.

Prerequisite: STAT 391

STAT 391 Probability Theory (2-2) 3

Sigma-algebra of events. Probability measure. Axioms of probability. Conditional probability and independence. Combinatorial problems. Random variables and their distributions. Functions of random variables. Distribution functions. Expectation. Conditional expectation. Moments and characteristic functions. Convergence of random variables. Central limit theorem. Laws of large numbers.

Prerequisite: STAT 154

STAT 444 Advanced Statistics Computing (3-0)3

Reading raw data files and Statistical Analysis Software (SAS) data sets, and writing the results to SAS data sets; subsetting data; combining multiple SAS files; creating SAS variables and recoding data values; creating listing and summary reports

Prerequisite: STAT 156 or consent of the department.

STAT 457 Statistical Design of Experiments (3-2) 4

Strategies for experimentation. Randomized complete and balanced incomplete block designs. Latin squares. General, two-level, and fractional factorials. Blocking and confounding in two-level factorials. Three and mixed level factorial and fractional factorials. Introduction to response surface methodology. Second-order experimental designs. Mixture experiments. EVOP. Robust design. Nonnormal responses. Unbalanced data in factorials. ANCOVA. Repeated measures.

Prerequisite: STAT 363

STAT 460 Nonparametric Statistics (3-0) 3

Review of basic statistics. Distribution-free statistics, ranking statistics, U statistics. Large sample theory for U statistics. Tests based on runs. Asymptotic relative efficiency of tests. Hypothesis testing, point and interval estimation. Goodness of fit, rank-order (for location and scale), contingency table analysis and relevant models. Measures of association, analysis of variance.

Prerequisite: STAT 272

STAT 461 System Simulation (3-2) 4

Introduction to discrete-event system simulation and simulation software. Statistical models in simulation. Queuing models. Input data modeling. Variance reduction techniques. Verification and validation of simulation models. Output analysis for a single model. Comparison and evaluation of alternative system design.

Prerequisite: STAT 291

STAT 462 Biostatistics (3-2) 4

Populations and samples. Types of biological data. Data transformations. Survival data analysis. Life tables. Sample size determination in clinical trials. Measures of association. The odds ratio and some properties. Application of generalized linear models and logistic regression to biological data. Analysis of data from matched samples.

Prerequisite: STAT 156

STAT 463 Reliability (3-0) 3

Reliability studies. Statistical failure models. Censoring and truncation and their types. Useful limit theorems in reliability. Inference procedures for lifetime distributions. System reliability. Bayesian methods. Accelerated life testing.

Prerequisite: STAT 272

STAT 464 Operations Research (2-2) 3

Basic operations research methodology. Basic models such as network flow models, project scheduling, dynamic programming, and production and inventory control. LP and game theory. Two person zero-sum games and saddle points.

Prerequisite: MATH 260

STAT 465 Multivariate Analysis I (3-0) 3

Vectoral representation of multivariate data. Sample mean vector and sample covariance matrix. Multivariate distributions, multivariate normal distribution, some other multivariate distributions. Parametric estimation. Hypothesis testing. Reduction of dimensionality.

Prerequisite: MATH 260, STAT 156

STAT 466 Multivariate Analysis II (3-2) 4

MANOVA. Principal components, factor analysis. Multivariate classification and clustering. Canonical correlation.

Prerequisite: STAT 465

STAT 472 Statistical Decision Analysis (3-2) 4

Introduction to decision making and types of decision situations. Bayes theorem and Bayesian decision theory. Prior, posterior and conjugate prior distributions. Loss functions. Empirical Bayesian approach. Utility theory for decision making. Value of information. Sequential decision procedures. Multidecision problems.

Prerequisite: STAT 154

STAT 477 Statistical Quality Control (2-2) 3

Introduction to concepts of quality and total quality management. Basic principles of  teamwork and learning. Probability in Quality Control. Methods and Philosophy of Statistical Process. Control Charts for variables and attributes. Cumulative-Sum and Exponentially Weighted Moving-Average Control Charts.  Process Capability Analysis.  Introduction to Experimental Design and Factorial Experiments. Taguchi Method, Lot-by-Lot Acceptance Sampling for attributes and by variables.

Prerequisite: STAT 156

STAT 479 Linear Programming (2-2) 3

Introduction to Linear Programming (LP). The simplex method. Transportation, assignment and transshipment problems. Sensitivity testing, duality theory and its applications. Advanced methods in LP and revised simplex algorithm.

Prerequisite: MATH 260

STAT 480 Application of Statistical Techniques in Socio-Economic Research (3-2) 4

Prinicipals of empirical socio-economic research. Formulation of research problems, determination of research design, application of sampling design. Strategies of field work, collection of data, improving data quality, selecting appropriate statistical methods. Evaluation of test of hypothesis and interpretation of findings. Preparation and presentation of a research proposal and report.

Prerequisite: STAT 356

STAT 482 Categorical Data Analysis (3-2) 4

Probability distributions and measures of association for count data. Inferences for two-way contingency tables. Generalized linear models, logistic regression and loglinear models. Models with fixed and random effects for categorical data. Model selection and diagnostics when response is categorical. Classification trees.

Prerequisite: STAT 272

STAT 487 Insurance and Actuarial Analysis (3-0) 3

Basic definition of insurance. Historical background. Insurance applications in government and private sector,  regulations and legislation in insurance. Fundamentals of insurance. Types of insurance, disaster insurance and risk menagement applications around the world. Turkish catastrophe insurance pool. Definition of risk, probability aspect of risk. Utility theory,  claim processes, distribution of claim processes.

Prerequisite: Consent of the department.

STAT 493 New Horizons in Statistics (3-0) 3

New advances in the field of statistics.

STAT 495 Applications in Statistics (2-2) 3

Applications of different statistical methods in various disciplines such as medicine, science, engineering and social sciences. Presentation of  projects involving these applications as group studies.

Prerequisite: STAT 156

STAT 497 Applied Time Series Analysis (3-2) 4

Time series as a stochastic process. Means, covariances, correlations, stationarity.  Moving averages and smoothing. Stationary and nonstationary parametric models.  Model specification. Estimation and testing. Seasonality. Some forecasting procedures. Elementary spectral domain analysis.

Prerequisite: STAT 272

STAT 499 Undergraduate Research (1-4) 3

This course is intended to improve the research capabilities of graduating students. Each student will be given a project and an academic advisor, lectures will be given on research design, data evaluation and report writing. A final report and/or seminar is required at the end of the semester.

Prerequisite: Consent of the department.